Improvements in feedback apparatus for stabilizing holograms

ABSTRACT

Method and apparatus for stabilizing the wave fronts at the recording plane of a hologram during hologram manufacture or while viewing a stored-beam interferogram. The disclosed system alleviates vibration isolation restrictions normally encountered with holographic work. A negative feedback system is utilized to monitor the change in intensity of a reconstructed optical wave front of light transmitted through or reflected from the hologram, relate such change to a known change in phase, and to phase modulate either the reference or signal beam accordingly. The intensity is monitored in either the signal beam or reference beam portion of the transmitted or reflected light. The wave fronts are controlled by adjusting the phase of either beam in accordance with a control signal. The negative feedback system includes a photodetector, a band-pass amplifier, a phase detector, a signal generator, a summing amplifier, a high voltage amplifier and an electro-optic phase modulator. Special purpose embodiments suitable for sampling local density fluctuation in a flowing gas are disclosed. Optional embodiments employing AC or DC stabilization circuits are presented.

United States ratent {IRU SS lilzl-tl'itNUE [72] inventors Charles Ray Pond Federal Way;

Patrick D. Texeira, Renton, both of Wash. [2]] Appl. No. 835,608 [22] Filed June 23, 1969 [45] Patented Nov. 23, 1971 [73] Assignee The Boeing Company Seattle, Wash.

[54] IMPROVEMENTS IN FEEDBACK APPARATUS FOR STABlLlZlNG HODOGRAMS 5 Claims, 6 Drawing Figs. [52] U.S, Cl 250/201, 250/2l8,250/225, 350/3.5,356/l06 [5 l] Int. Cl G01] 1/20, G0ln2l/26.G02b [50] Field ofSeaieh .i 250/201, .218, 225; BSD/3.5; 356/l06 [56] References Cited UNIT ED STATES PATENTS 3,494,698 2/1970 Neumann 350/3.5 X OTHER REFERENCES Neumann et al., improvement of Recorded Holographic Fringes by Feedback Control, June 1967, Applied Optics, pp. l097- l I04, Vol. 6, No. 6

enrich Rona Primary Examiner-Archie R. Borchelt Assislanl Examineh-T. Ne Grigsby Allorneys-Glenn Orlob, Bernard Donahue and Kenneth W.

Thomas ABSTRACT: Method and apparatus for stabilizing the wave 'fronts at the recording plane of a hologram during hologram manufacture or while viewing a stored-beam interfcrogram, The disclosed system alleviates vibration isolation restrictions normally encountered with holographic work. A negative feedback system is utilized to monitor the change in intensity of a reconstructed optical wave front of light transmitted through or reflected from the hologram, relate such change to a known change in phase, and to phase modulate either the reference or signal beam accordingly. The intensity is monitored in either the signal beam or reference beam portion of the transmitted or reflected light. The wave fronts are controlled by adjusting the phase of either beam inaccordance with a control signal. The negative feedback system includes a photodetector, a band-pass amplifier, a phase detector, a signal generator. a summing amplifier, a high voltage amplifier and an elcctro-optic phase modulator. Special purpose embodiments suitable for sampling local density fluctuation in a flowing gas are disclosed. Optional embodiments employing AC or DC stabilization circuits are presented.

potential difficulty methods to nonlaboratory uses, such Oplics, 6, June energy can be sampled, and cost and complexity of electronic and optical components.

Holography is; a method for recording the amplitude and phase. of

sional properties of the holographic reconstruction.

The general holographic method, invented by Gabor (D. Gabor, Proceedings Royal Society, London, A197, 454, 1947; Proceedings Physical Society, London, B64, 449, improved by Leith and Upatnieks (F. Leith and J. Upatnieks, Journal Optical Sociely of America, 54, pg. 1,295,

The following mathematical analysis describes the holographic process and clarifies the extension to the state of the art made possible by our invention.

The signal beam and reference beam at the holographic recording plane can be represented in the usual complex notations as follows:

where a, and a, are the amplitudes of the signal and reference beams at the point (x,y) and lb, and 1), are their phases. The optical radian frequency is w, and r is time.

The recording medium responds to the incident intensity, I, where in an ideal holographic recording medium. the amplitude transmittance afler developing is a linear function of the incident intensity during exposure, as expressed by the relation:

T,,==T +kl where 7}, is the amplitude transmittance after developing, and T and k are constants which depend on the particular recording medium employed.

When the developed hologram is illuminated by just the reference beam, the waves transmitted through the hologram are given by rT,,=rT +rkl The first term, rT is simply the reference beam attenuated by the hologram. The second term can be expanded as follows:

where the cos(,,) term has been expressed in exponential form. After clearing fractions and multiplying out the final term,

rk#rk(a, +zz, )+ka,a,e*"? "-Hca ap The middle term is just the original signal beam weighted by the factor ka}, thus the hologram reconstructs the signal beam when illuminated only by the reference beam.

The preceding discussion is the usual analysis of the holographic process. The following analysis pertains to our invention.

Suppose the phase of the reference beam is modulated by a time varying function, (r), then the expression of the reference beam is The phase modulation can be accomplished in several ways, for instance with an electro-optic modulator, an acoustic modulator, or a mechanically driven mirror.

The reconstructed signal beam is again rT,,=rT,,+rkI, but now,

y a s xwi+. g (Ul k r2 lur!+2rl+tlll inspection of the second term reveals that the phase of the reconstructed signal beam is modulated with the same time varying function, (I), that describes the phase modulation of the reference beam. It is important to notice that the phase modulation of the reconstructed signal beam is independent of the position (x,y) on the hologram. The phase changes by the same amount over the entire hologram. When the hologram is recorded on a self-developing medicase of a photochromic material used in the photobleaching mode, this is the condition required to correct for the phase 3 perturbations and stabilize the wavefronts at the recording plane. If the recording material is used in the photodarkening mode, the reconstructed waves should be 180 out of phase with the direct signal waves. so the stability condition is Although it has been assumed for purposes of discussion that N!) is a phase modulation of the reference beam, it should be noticed that the expression for I. and the stability conditions are unchanged if I (t) is a phase modulation of the signal beam. The phase modulator can beplaced in either beam. It should also be noticed that the preceding discussion is applicable to stabilization of the wavefront while viewing a stored-beam holographic interferogram.

One other relationship is important for understanding the operation of this invention. The expression for I, can be differentiated to yield Consider. for example, a photobleached hologram where the stability condition (I)+A,+A I ,=0 The derivative above shows that I, increases when is increased while (I)+A,+A I is negative, and 1, decreases when b(!) is increased while d (t)+A I ,+A,. is positive, 'rr/2 The amount of change of I for a given change of I (1) depends on the instantaneous magnitude of I (r)+A,+A,. Thus, both the magnitude and direction of the total phase perturbation of both beams can be determined by measuring only the change in I, due to a known change in the phase of either the reference or signal beam. Furthermore. as was shown earlier, the total phase perturbation can be eliminated by adjusting the phase of either beam.

It is the object of this invention to provide a method and apparatus for controlling and stabilizing the wavefronts at the plane of a hologram during recording or while viewing a stored-beam holographic interferogram, thereby removing the restriction on vibration isolation normally encountered with holographic work and allowing the use of holographic methods in previously inaccessible environments.

The above objective is achieved by monitoring the change in intensity of't'he light transmitted through or reflected from the hologram, and relating said change in intensity to a known change in phase of either the signal beam or the reference beam. The intensity can be monitored in either the'signal beam or reference beam portions of the transmitted or reflected light. The wavefronts are controlled by adjusting the phase of either beam in accordance with a control signal derived by monitoring changes in light intensity.

The differences between our invention and the technique used in the Neumann and Rose publication referenced previously, will be apparent to those skilled in the art. In the referenced publication, the photodetector senses the interference pattern betweenv the-signal beam and the reference beam. In fact, a slit is used to limit the pattern to a single fringe. ln out invention, the error signal is derived from interference between a direct beam (either a signal beam or reference beam) and a reconstructed beam. ln systems in which the closed loop does not include all of the optical elements it is possible to have instability at the recording medium even though the hologram fringes are stabilized at the photomultiplier. This problem does not exist in our invention. Furthermore, as was noted previously, in the referenced technique only a small fraction of the available energy is sampled. All of the energy available can be used with our invention, resulting in increased accuracy and simplification of the electrical and optical components. Additional differences in our invention and the apparatus discussed in the referenced publication will become apparent in the discussion which follows.

FIG. 1 schematically depicts a preferred embodiment of a hologram stabilizationapparatus utilizing a negative feedback control system constructed according to the teachings of this disclosure. 1

FIG. 2 is a plot of the intensity and phase relationship when phase modulation is about the point ofzero-phase difference.

FIG. 3 is a plot of the relationship between intensity and phase difference when the phase modulation is about the positive slope of the intensity curve.

FIG. 4 is a plot of the relationship between intensity and phase difference when the phase modulation is about the negative slope of the intensity curve.

FIG. 5 relates to a special embodiment of the invention which is designed to sample local density fluctuation in a flowing gas.

FIG. 6 is a schematic of an optical embodiment similar to that shown in FIG. 5 wherein the AC stabilization has been replaced by a DC stabilization feedback loop.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. I is a schematic of a preferred embodiment of the stabilization system wherein light from the laser 2 is divided into a reference beam R and a signal beam S by the beam splitter 4. The reference beam R is reflected from the mirror 6 to the electro-optic phase modulator 8, and subsequently reflected by mirror 10 and prism l2 onto the hologram recording media 14. The signal beams is expanded with the lens 16 and collimated by lens 18. The collimated signal beam S reflects offthc test surface 20 through lens 18 and into prism 12. The prism 12 reflects the reference beam R and the signal beam S onto the hologram recording material 14. The hologram recording material 14 is preferably a self-developing material, such as a photochromic plastic or photographic material pretreated with a developer solution.

The interaction of the signal beam S and the reference beam R with the hologram recording material 14 gives rise to a reconstructed signal beam RS, which propagates along with the signal beam S. The lens 22 images the signal beam S and the reconstructed signal beam RS, at the image plane 24. Part of the superimposed beams (S+RS), is reflected by the beam splitter 26 onto the photodetector 28.

The electronic circuitry consists of a negative feedback system. The output 30 of the photodetector 28 is amplified and filtered by the band-pass amplifier 32. The phase of the band-pass amplifier output 34 is detected by the phase detector 36. The phase detector 36 compares the phase of the signal 34 to the phase of a 4.3 kilohertz signal 38 from the signal generator 40 The phase detector 36 has a low pass filter which removes the 4.3 kilohertz carrier and passes demodulated phase information. The output 42 of the phase detector 36 is a voltage which varies with the amplitude and phase of the 4.3 kilohertz component of signal 34. The signal 42 is added to an alternating 4.3 kilohertz signal 44 from the signal generator 40 by the direct coupled summing amplifier 46. The output 48 of the summing amplifier 46 is further amplified by the high-voltage direct-coupled amplifier 50 and the resulting signal 52 is applied to the electro-optic phase modulator 8.

The electro-optic phase modulator 8 adjusts the phase of the reference beam R to compensate for environmentally induced phase perturbation of both beams R and S. The amount .of allowable change in phase between the reference and signal beams can be controlled by the loop gain of the feedback system.

FIGS. 2 through 4 present graphic plots of the equation previously derived describing the relationship between the intensity l,. and the phase difference between the direct and reconstructed wave front during interferometric use of a stored-beam hologram.

Ifa change in intensity occursdue to phase perturbation in either the direct or reconstructed wave fronts, the intensity can be maintained at some desired reference level by changing the phase of either wave front. When recording a stored-beam ologram. the intensity is changing as a function of time, thus the coefficients A and B of the general equation previously FIGS. 2 through 4.

Although the FIG. I embodiment utilizes AC feedback control for stabilization, it should be noted that DC stabilization have been used for the reconstruction stage. In DC statered. amplified, and applied to an electro-optic lator. I

For AC stabilization, which is the stabilization used in the FIG. I embodiment and is applicable to both recording and reconstructing of the hologram, the phase of the optical reference beam is modulated by a sinusoidal voltage at the optical phase modulator. The frequency of 4.3 kHz. is used for convenience. The only requirement placed on the modulating frequency is that it be a frequency which is not within the range of frequencies which the compensate for.

A sinusoidal waveform was used for convenience. Other waveforms may be used. Modulation depth was approximately 1r/9 radians. The effect of output ofthe photodetector is shown in FIGS. 2 through 4.

Referring now to FIG. 2, the phase modulation 59 is about the point of zero-phase difference. Since the slope of the response characteristic 60 negative slope of the response characteristic 60. Note the difference in phase angle between the detector outputs 64 and 66 for phase modulation of the positive and negative slopes ofthe response characteristic.

Comparison of the signal from the detector with the reference modulation applied to the electro-optic phase modulator determines the phase relationship between the direct and reconstructed wave fronts. Comparison of these two signals in a phase detector which is also amplitude sensitive, results in an error signal which can be used in a closedloop negative feedback system to maintain a small error in optical phase angle. Other feedback techniques can be used to make this error approach zero.

The negative-feedback system utilized in the FIG. I. embodiment will maintain adequate error margin thereby normally precluding a requirement for a more sophisticated feedback system. The system can be locked to either the crest or the valley of the intensity curve by changing the phase of the reference modulation by 1r radians.

It will be readily understood by those skilled in this art that the higher order harmonic components present at the detector output could also be used for stabilization purposesJfan even harmonic is used, the detector output will be maximum when the phase error is zero.

The lock-in range is limited by the dynamic range of the system. The optical phase modulator usually limits the dynamic range constraining control to a limited number of wavelengths or to fractions ofa wavelength. For a system with remains small within the dynamic range. If the dynamic range is exceeded. the system maintains a small error for an equivalent wavelength change of one wavelength and approaches an error ofa one-fourth wavelength for the next onefourth wavelength of equivalent wavelength change.

phase modulation on the voltage is zero, the detector output 62 con- The AC technique of wave front stabilization disclosed in FIG. I has advantages over the DC technique. since it is applicable to both reconstruction and recording of the storedbeam hologram. The DC technique. however, is susceptible to changing intensity at the detector during recording. whereasthe AC system will maintain stability as the recording process takes place. As has been pointed out in the preceding theoretical discussion, it should be noted that a wide class of periodic and aperiodic phase perturbations can be used to effect stabilization in accordance with the teachings ofthis disclosure.

' FIGS. 5 and 6 relate to another embodiment of this invention wherein the hologram stabilization apparatus is used to stabilize the fringes of a holographic interferometer, thereby ofthe response characteristic.

FIG. 5 is a schematic of the optical and electronic elements used with AC stabilization.

FIG. 6 is a schematic of the optical and electronic elements employing DC stabilization.

The particular variation of holographic interferometer shown in FIGS. 5 and 6 is designed to sample local density fluctuations in a flowing gas. As will be recognized by those skilled in the art, the use ofa hologram in place ofthe final interferometer beam splitter eliminates the effect of aberrations inherent in this very fast (lowf-number) optical system. This focused beam interferometer is preferentially sensitive to small-scale density fluctuations at focus-sincc, in this region, the optical phase is altered across the entire signal beam cross section. A small-scale density fluctuation outside the focal region affects only a portion of the beam cross section, resulting in a proportionate'reduction in the change in optical phase.

Referring now to FIG. 5, the laser I01 emits a beam of coherent, plane polarized light. This beam is divided by beam splitter I03 into the test beam T and reference beam R. Test beam T reflects off mirror I05 and passes through quarterwave retardation plate 107. Retardation plate I07 changes the polarization of the test beam from linear to circular polarization. Test beam T is then expanded by lens I09 to fill the-aperture oflens III. Lens III focuses test beam T within the test section 113. The test beam T is collected by lens I15 and impinges on the hologram II7. The hologram 117 is recorded and processed prior to operation of the test section; Retardation plate 107 is ordinarily removed while recording the hologram 117.

Reference beam R, after I19, expanding lens hologram 117. Part passing through phase modulator I21 and prism I23, also impinges on the of the reference beam R is diffracted by the hologram 117 into a plane polarized reconstructed test beam RT. The reconstructed test beam RT and the transmitted portion of the test beam T are incident on the calcite prism 125.

The calcite prism I25 is oriented with its optical axis normal to the nominal beam direction and rotated 45 from the plane of polarization ofthe reconstructed test beam RT so as to exploit the well-known property of double refraction. In this manner the optical power in the reconstructed reference beam is divided equally into the ordinary beam 0 and extraordinary beam E. The test beam T is also divided equally into the ordinary beam 0 and extraordinary beam E. However, since the test beam is circularly polarized, the O and E components of the test beam are out of phase. The doubly refracted beams O and E fall respectively on stabilization detector I27 and output detector 129. The feedback electronics 133439 -are adjusted to hold detector I27 at a minimum of the (Again, the hologram is recorded The operation of the stabilization electronics 133-139 is similar to that used in FIGS. 1-4. The center frequency is determined by the oscillator 133. The oscillator voltage applied to the modulator v1 19 causes a phase modulation of the reference beam R. The phase modulation is detected with detector 127 and amplified by band-pass amplifier 135. The passband of amplifier 135 determines the high-frequency cutoff of the stabilization loop. The density fluctuations of interest in the test section 113 occur at frequencies above the amplifier 135 bandwidth.

Phase detector 137 generates an error signal depending on the phase difference of the output signals of oscillator 133 and amplifier 135. The low-frequency error signal is amplified by the modulator driver 139 and applied to the modulator 119.

The AC stabilization method is used primarily for investigating high frequency density fluctuations associated with acoustic noise generation. As mentioned before. the use of AC stabilization (as opposed to DC stabilization) eliminates problems caused by drift. However, the apparatus shown in FIG. can be used with DC stabilization. as shown in HO. 6. The -DC stabilization offers certain advantages when investigating low frequency density fluctuations.

Referring now to FIG. 6, the quarter-wave retardation plate 107 of FIG. 5 is replaced by half-wave retardation plate 108.

and processed with the retardation plate 108 removed.) The retardation plate 108 is adjusted to impart 90 rotation of the plane of polarization ofthe test beam T. The overall effect of this change in polarization of the test beam is that the intensities of beams O and E are now |80 apart on the response characteristic rather than 90 apart.

The beams O and E are detected with two detectors in detector assembly 128. The detector output is coupled into bridge circuit 130. The bridge circuit provides an error voltage depending on the difference in intensities ofO and E, The error voltage is amplified by the feedback amplifier 134 and applied to modulator 119 by modulator driver 139. The modulator 119 responds to equalize the intensities O and E. The output voltage 131 is shown coupled out ofthe bridge circuit, although in practice the output may be coupled out at other points of the feedback loop, such as at the output of feedback amplifier 134. Depending on the method of output coupling, it is possible to substantially reduce the effects of laser amplitude variation.

What is claimedis:

1. ln apparatus for development or viewing of a hologram which includes means for generating two direct beams of coherent light and for passing one of said beams through said hologram to thereby create a reconstructed wave front by the interaction of said one of said beams with said hologram, an improved closed-loop system for stabilizing the wave fronts at the plane of said hologram comprising: light-sensitive means, positioned in the path of light from said reconstructed wave front and said one of said beams, for sensing the combined light intensity of a portion of said reconstructed wave front and said one of said beams; means for producing an output signal proportional to said combined light-intensity; means responsive to said output signal for adjusting the phase of one of said two direct beams to stabilize the wave fronts at the plane of said hologram, means for changing the relative state of polarization of said two direct beams and means for focusing one of said beams onto a position within a specimen to be examined; wherein said means for sensing includes means utilizing the property of double refraction to divide light into two portions.

2. Apparatus according to claim 1 wherein said means for changing the relative state of polarization includes means for changing the polarization of one of said two direct beams from linear to circular.

3. Apparatus according to claim 1 wherein said means for changing the relative state of polarization includes means for changing the planes of polarization so that said planes are approximately orthogonal.

. An apparatus ofthe class described comprising means for generating two direct beams of coherent light, means for generating a reconstructed wave front by passing one of said direct beams through a hologram, and means for stabilizing the wave fronts at the recording plane of said hologram, said means for stabilizing comprising: means for generating a selected periodic signal; means responsive to the combined light intensity of said reconstructed wave front and said one of said direct beams to effect an output signal; means responsive to said output signal for producing a second output signal which has been filtered to a selected frequency bandwidth;

graphic medium positioned for development or viewing of a hologram, means for passing one ofsaid beams through said hologram to create a reconstructed wave front through the interaction ofsaid one ofsaid beams with said hologram an improved closed loop system for stabilizing the wave fronts at the recording plane of said hologram comprising: light-sensitive means positioned for sensing the combined light intensity ofa portion of said reconstructed wave front and said one of said beams; band-pass filtering means, operably connected to said light-sensitive means, for producing an electrical output signal proportional to said light intensity and filtered to a selected frequency range; signal generator means for generating an electrical periodic signal; optical phase modulator means, responsive to said periodic signal, for modulating the phase of one of said beams; electrical signal phase detector means for comparing the phase and amplitude of said output signal and said periodic signal and for generating an error signal proportional to the phase difference between said output and said periodic signal; and means responsive to said error signal for adjusting the phase of one of the said beams to stabilize the wave fronts at the plane of said hologram.

i i i 

1. In apparatus for development or viewing of a hologram which includes means for generating two direct beams of coherent light and for passing one of said beams through said hologram to thereby create a reconstructed wave front by the interaction of said one of said beams with said hologram, an improved closedloop system for stabilizing the wave fronts at the plane of said hologram comprising: light-sensitive means, positioned in the path of light from said reconstructed wave front and said one of said beams, for sensing the combined light intensity of a portion of said reconstructed wave front and said one of said beams; means for producing an output signal proportional to said combined light intensity; means responsive to said output signal for adjusting the phase of one of said two direct beams to stabilize the wave fronts at the plane of said hologram, means for changing the relative state of polarization of said two direct beams and means for focusing one of said beams onto a position within a specimen to be examined; wherein said means for sensing includes means utilizing the property of double refraction to divide light into two portions.
 2. Apparatus according to claim 1 wherein said means for changing the relative state of polarization includes means for changing the polarization of one of said two direct beams from linear to circular.
 3. Apparatus according to claim 1 wherein said means for changing the relative state of polarization includes means for changing the planes of polarization so that said planes are approximately orthogonal.
 4. An apparatus of the class described comprising means for generating two direct beams of coherent light, means for generating a reconstructed wave front by passing one of said direct beams through a hologram, and means for stabilizing the wave fronts at the recording plane of said hologram, said means for stabilizing comprising: means for generating a selected periodic signal; means responsive to the cOmbined light intensity of said reconstructed wave front and said one of said direct beams to effect an output signal; means responsive to said output signal for producing a second output signal which has been filtered to a selected frequency bandwidth; means for detecting the phase and amplitude of said second output signal to effect a control signal; and means responsive to said control signal and said periodic signal for phase modulating one of said beams to reduce the relative phase difference between said reconstructed wave front and said one of said beams at said recording plane.
 5. In apparatus of the class described which includes means for generating two direct beams of coherent light, a holographic medium positioned for development or viewing of a hologram, means for passing one of said beams through said hologram to create a reconstructed wave front through the interaction of said one of said beams with said hologram, an improved closed loop system for stabilizing the wave fronts at the recording plane of said hologram comprising: light-sensitive means positioned for sensing the combined light intensity of a portion of said reconstructed wave front and said one of said beams; band-pass filtering means, operably connected to said light-sensitive means, for producing an electrical output signal proportional to said light intensity and filtered to a selected frequency range; signal generator means for generating an electrical periodic signal; optical phase modulator means, responsive to said periodic signal, for modulating the phase of one of said beams; electrical signal phase detector means for comparing the phase and amplitude of said output signal and said periodic signal and for generating an error signal proportional to the phase difference between said output and said periodic signal; and means responsive to said error signal for adjusting the phase of one of the said beams to stabilize the wave fronts at the plane of said hologram. 